On the determination of equilibrium constants 1 Marcel Maeder University of Newcastle, Australia

Chemometrics The ultimate goal of curve resolution would be to be able to determine the number of components in an overlapping chromatographic peak as well as the spectrum and concentration profile of each compound, without assumption regarding peak shape, location, or identity. Michael F. Delaney: Chemometrics Anal. Chem. 1984, 56, 261R-277R 2

The law of mass action 3 X, Y, Z are called components All X x Y y Z z are called species (components X, Y, Z are also species)

4 If [X x Y y Z z ], [X], [Y] and [Z] are known, the determination of β xyz is very easy. However this is rarely the case. The law of mass action

Case 1: Fe 3+ /SCN - 5 Only Fe(SCN) 2+ absorbs in the visible. If its molar absorptivity ε is known, it is possible to determine [Fe(SCN) 2+ ] from absorbance. Further, [Fe 3+ ] tot and [SCN - ] tot are known, thus: [Fe 3+ ]= [Fe 3+ ] tot - [Fe(SCN) 2+ ] [SCN - ]= [SCN - ] tot - [Fe(SCN) 2+ ]

Case 1: Fe 3+ /SCN - 6 Issue: how can ε be determined? Large excess of SCN -, then all Fe 3+ exists as [Fe(SCN) 2+ ] ??? However, there might/will be formation of [Fe(SCN) 2 + ] which also absorbs with unknown molar absorptivity. We will come back to this system.

Titrations 7 Preparation of a series of solutions with different total concentrations of the components. a) Manual preparation [X] tot,1 [Y] tot,1 [X] tot,1 [X] tot,2 [Y] tot,2 [X] tot,2 [X] tot,3 [Y] tot,3 [X] tot,3 [X] tot,n [Y] tot,n [X] tot,n … One or several properties of each solution are measured e.g. pH UV-Vis spectrum IR spectrum NMR spectrum etc.

Titrations 8 b) automatic preparation One or several properties of each solution are measured e.g. pH UV-Vis spectrum IR spectrum NMR spectrum etc.

Case 2: pH titration 9 The measurement is pH vs addition of reagent pH = -log[H + ], thus the ‘measurement’ is [H + ]

Case 2: pH titration 10 Two protonation equilibria at secondary amines Amide nitrogens are not basic, no protonation H+H+ H+H+ H+H+

Case 2: pH titration 11 Determination of β 110 and β 120 : Systematically change values until the fit is optimal.

Fitting 12 Systematically change parameters until the fit is optimal: a)calculate all species concentrations from total concentrations and initial guesses for equilibrium constants (Newton Raphson) b)Compare computed curve with measured (residuals) c)Change parameters systematically (Newton-Gauss- Marquardt)

Newton-Raphson 13 Example: Cu 2+ ethylene diamine, en protons, H + [Cu 2+ ] tot [en] tot [H] tot [Cu 2+ ], [en], [H]; [enH], [enH 2 ], [Cu(en)], [Cu(en) 2 ], [Cu(en) 3 ], [Cu(en)H], [Cu(en)OH] and [OH - ] need to be calculated

Newton-Raphson species: M, L, and H; HL, H 2 L, ML, ML 2, ML 3, MLH, MLH -1 and OH. 11 equations 1 solution !

Newton-Raphson 15 V_add (mL) LHCu E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-03 Species Concentrations V_add (mL)L HCuLHLH2CuLCuLOHCuLOH2OH E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-03 Component Concentrations

residuals, pH titrations r = pH meas - pH calc 16 pHpH_calc pH calc =-log([H+])

residuals, spectrophotometric titrations R = D meas – D calc D calc = C × A = C × C + D ( = C × C/D) 17 AC R

Newton-Gauss-Marquardt 18

Fitting using the solver (excel) 19 e.g. H 3 PO 4

Fitting using the solver (excel) 20 For 2-component protonation equilibria it is possible to explicitely calculate the volume for a given pH. Calculation of x for a given value of y. Can be done in excel.

Fitting using the solver (excel) 21 The curve is calculated as a function of the parameters

Fitting using the solver (excel) 22 The measured curve is compared with the calculated curve, the parameters are changed until the fit is optimal. Manually or better with solver

Fitting using the solver (excel) 23 The measured curve is compared with the calculated curve, the parameters are changed until the fit is optimal. Manually or better with solver

Fitting using the solver (excel) 24 Fitting only the concentration of the acid

Fitting using the solver (excel) 25 Fitting the concentration of the acid and the protonation constants >>> perfect fit

Example 1 : Fe 3+ /SCN - Fe(SCN) 2+ characteristic dark brown colour, used to detect either Fe 3+ or SCN Inorganica Chimica Acta 445 (2016) 155–159

Example 1 : Fe 3+ /SCN - There are 2 problems: a) potential formation of additional complexes 27

Example 1 : Fe 3+ /SCN - change in λ max is indicative of additional species, rank>1 28

Example 1 : Fe 3+ /SCN - The other problem: b) Complex is not stable, unknown decomposition reactions 29 Absorbance at 458 nm against time for different SCN - concentrations; (a) with a linear, (b) with a logarithmic time scale.

Measurements, stopped- flow [SCN - ] [Fe 3+ ] [HClO 4 ]

Example 1 : Fe 3+ /SCN - solution: Stopped-flow experiment, measure spectrum as a function of time, analyse and calculate spectrum at time=0. 31 Experimental (points) and calculated (lines) absorbances against time for 1.5×10 -4 M Fe 3+ and 0.25 M SCN - ; (a) with a linear, (b) with a logarithmic time scale.

Example 1 : Fe 3+ /SCN - solution: Stopped-flow experiment, measure spectrum as a function of time, analyse and calculate spectrum at time=0. 32

Example 1 : Fe 3+ /SCN - 33 Species concentration against total thiocyanate concentration, total [Fe 3+ ] = 1.5×10 -4 M at ionic strength 0.5 M. Legend: M=Fe 3+ ; ML=FeSCN 2+ ; ML2=Fe(SCN) 2 + ; MOH=FeOH 2+ ; LH=HSCN.

Example 1 : Fe 3+ /SCN - 34 YearRef.TechniqueT/ o CIS/M K 1 /M -1 /nm / L mol -1 cm -1 K 2 /M -1 /nm / L mol -1 cm [2]Spectro [7]Spectro [10]Spectro [5(c)]Spectro [6(a)]Potent [3]Spectro Potent [5(d)]Spectro [5(h)]Spectro [6(b)] Stopped- flow Spcctro [6(c)]Spectro [6(d)]Spectro Current work Spectro, stopped- flow ±14587±1485

Example 1 : Fe 3+ /SCN - 35

Example 2 : MEA + CO 2 36 How can this process be observed and analysed quantitatively?

Example 2 : MEA + CO 2 37 How can this process be observed and analysed quantitatively? a)Potentiometric titration (as there are protonation equilibria) No, reactions too slow b)Spectrophotometric titration, with long equilibration No, no useful spectra (unless IR) c) 1 H-NMR yes

Example 2 : MEA + CO 2 38 Total concentration of MEA, CO 3 2-, H + are known Relative concentrations of MEA/MEAH + and carb - /carbH from NMR integrals

Example 2 : MEA + CO 2 39 [MEA/MEAH + ] [carb - /carbH] o, x, ◊ integrals of peaks _______ fitted curves K 7 = 204 ± 5 log K 8 = 7.49 ± 0.05

Example 2a : MEA + CO 2 40 K 7,NMR = 204 ± 5 Kinetic determination (wait for next presentation ) log K 7,NMR = 2.31 ± 0.01 log K 7,kin = 2.69 ± 0.02 ? 

Example 3: morpholine + CO 2 41

morpholine + carbamate Example 3: morpholine + CO 2

1 H-NMR spectra of Morpholine at 25˚C (Morpholine/Na 2 CO 3 1/2 with different volumes of 5M HCl)

Analysis of the data

Result of the Analysis

carbamate and carbamic acid

Example 4: Cu 2+ + DANA potentiometric titrations

Example 4: Cu 2+ + DANA potentiometric titrations First the protonation of the ligand has to be determined H+H+ H+H+ No protonation of the amide groups

Example 4: Cu 2+ + DANA potentiometric titrations 10ml.005 M DANA in 0.191M HCl Titrated with M NaOH

Example 4: Cu 2+ + DANA potentiometric titrations The model, with fitting results

Example 4: Cu 2+ + DANA potentiometric titrations calculated concentrations vs pH and ml added

Example 4: Cu 2+ + DANA potentiometric titrations 2 nd titration in the presence of Cu 2+

Example 4: Cu 2+ + DANA potentiometric titrations 10ml.005 M DANA, M Cu 2+ in 0.191M HCl Titrated with M NaOH

Example 4: Cu 2+ + DANA potentiometric titrations Fitting both titration curves together

Example 4: Cu 2+ + DANA potentiometric titrations calculated concentrations vs pH and ml added

ReactLab pH gamma L is ethylene diamine, H 2 N-CH 2 -CH 2 -NH 2 Activities not concentrations: {L} not [L]

ReactLab pH gamma

Ammonia as amine for PCC aqueous solutions of amines

Ammonia as amine for PCC Ammonia has many advantages, compared to MEA: high capacity no degradation in presence of O 2 cheap less corrosive low energy requirement Main disadvantage high volatility

Ammonia as amine for PCC Main disadvantage high volatility What can be done about it? Addition of loss supressants organic compounds that form hydrogen bridges metal ions

Ammonia as amine for PCC Addition of metal ions indeed reduces the vapor pressure of ammonia

Ammonia as amine for PCC Calculations with a complete equilibrium model reveals that it is just the reduced free [NH 3 ] that results in the reduced loss, as efficient as using less ammonia

Henry coefficient for CO 2 For a simple gas, nonreactive, H N2 can be calculated if the partial pressure p N2 in the gas phase and the concnetration [N 2 ] in the liquid phase are known. [N 2 ] p N2

Henry coefficient for CO 2 For a reactive gas, like CO 2, the partial pressure p CO2 in the gas phaseis easy to determine but the concentration [CO 2 ] in the liquid phase is very difficult to determine p CO2 [CO 2 ] carbon dioxide [H 2 CO 3 ]carbonic acid [HCO 3 - ] bi-carbonate [CO 3 2- ] carbonate [MEACOOH] carbamic acid [MEACOO - ] carbamate

Henry coefficient for CO 2 The approach chosen by chemical engineers: determine H N2O the ratio r is constant for all solvents H CO2 can be calculated fron H N2O !!!

Henry coefficient for CO 2 The chemistry approach: Calculate [CO 2 ] from all the equilibrium constants and determine H CO2. p CO2 [CO 2 ] carbon dioxide [H 2 CO 3 ]carbonic acid [HCO 3 - ] bi-carbonate [CO 3 2- ] carbonate [MEACOOH] carbamic acid [MEACOO - ] carbamate

Henry coefficient for CO 2 There are some 1000 data sets published many inconsistencies p CO2 [CO 2 ] tot [MEA] tot At many temperatures

Henry coefficient for CO 2 many inconsistencies: p CO2 [CO 2 ] tot 0-3 M [MEA] tot 2.5 M 40 C

Henry coefficient for CO 2 many inconsistencies: p CO2 [CO 2 ] tot 0-3 M [MEA] tot M C

Chemistry - Metrics Michael F. Delaney: Chemometrics Anal. Chem. 1984, 56, 261R-277R 70

kheili mamnoon 71

kheili mamnoon 72

73 CbCb C a, V a pH